$\dfrac{ -4x - 10y }{ 5 } = \dfrac{ -3x - z }{ 6 }$ Solve for $x$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -4x - 10y }{ {5} } = \dfrac{ -3x - z }{ 6 }$ ${5} \cdot \dfrac{ -4x - 10y }{ {5} } = {5} \cdot \dfrac{ -3x - z }{ 6 }$ $-4x - 10y = {5} \cdot \dfrac { -3x - z }{ 6 }$ Multiply both sides by the right denominator. $-4x - 10y = 5 \cdot \dfrac{ -3x - z }{ {6} }$ ${6} \cdot \left( -4x - 10y \right) = {6} \cdot 5 \cdot \dfrac{ -3x - z }{ {6} }$ ${6} \cdot \left( -4x - 10y \right) = 5 \cdot \left( -3x - z \right)$ Distribute both sides ${6} \cdot \left( -4x - 10y \right) = {5} \cdot \left( -3x - z \right)$ $-{24}x - {60}y = -{15}x - {5}z$ Combine $x$ terms on the left. $-{24x} - 60y = -{15x} - 5z$ $-{9x} - 60y = -5z$ Move the $y$ term to the right. $-9x - {60y} = -5z$ $-9x = -5z + {60y}$ Isolate $x$ by dividing both sides by its coefficient. $-{9}x = -5z + 60y$ $x = \dfrac{ -5z + 60y }{ -{9} }$ Swap signs so the denominator isn't negative. $x = \dfrac{ {5}z - {60}y }{ {9} }$